Solve for $x$ : $4\sqrt{x} + 6 = 7\sqrt{x} + 10$
Solution: Subtract $4\sqrt{x}$ from both sides: $(4\sqrt{x} + 6) - 4\sqrt{x} = (7\sqrt{x} + 10) - 4\sqrt{x}$ $6 = 3\sqrt{x} + 10$ Subtract $10$ from both sides: $6 - 10 = (3\sqrt{x} + 10) - 10$ $-4 = 3\sqrt{x}$ Divide both sides by $3$ $\frac{-4}{3} = \frac{3\sqrt{x}}{3}$ Simplify. $-\dfrac{4}{3} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.